empowerment

**Empowerment** is an **intrinsic motivation signal that measures the agent's ability to influence its future sensory states** — defined as the channel capacity (maximum mutual information) between the agent's actions and its future states: $I^*(A_t; S_{t+k})$. **Empowerment Formulation** - **Mutual Information**: $mathfrak{E}(s) = max_{p(a|s)} I(A_t; S_{t+k} | S_t = s)$ — maximize over all action distributions. - **Channel Capacity**: Empowerment is the information-theoretic channel capacity of the action → future state channel. - **High Empowerment**: States where the agent's actions have the most diverse consequences — the agent has maximum control. - **Low Empowerment**: States where actions have little effect — the agent is "stuck" or "powerless." **Why It Matters** - **Task-Independent**: Empowerment is a universal intrinsic motivation — no task-specific reward needed. - **Meaningful Behavior**: Empowerment-seeking agents naturally move to states of high influence — homeostasis, tool use, position maintenance. - **Safety**: Empowerment can keep agents in controllable, recoverable states — useful for safe RL. **Empowerment** is **seeking maximum influence** — moving to states where the agent's actions have the greatest impact on its future.